1135
Conformational Isomerism in 1-Substituted Derivatives of 3,3-Dimethylbutanel George M. Whitesides, John P. Sevenair, and Rudolph W. Goetz Contributionf r o m the Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. Received August 3,1966 Abstract: The difference in energy between gauche and trans conformers of several 1-substituted 3,3-dimethyl-
butanes has been determined using nmr spectroscopy. The relative order of “size” of the substituent groups estimated from these energy differences is significantlydifferent from that obtained from previous studies of the equilibria between axial and equatorial conformers of the corresponding substituted cyclohexanes.
T
he conformational analysis of acyclic organic molecules has been explored less systematically than that of alicyclic compounds, in part because the former isomerism has proved the more difficult to investigate experimentally. 2, In consequence, most data dealing with the general problem of the influence of substituents on conformational equilibra, and with the particular problem of the proper relative “sizes” to be assigned to common organic groups, have been obtained by examination of the influence of these groups on the conformations of cyclohexane rings. It is not presently clear to what extent these data are applicable to other types of conformational problems. Nuclear magnetic resonance spectroscopy provides an attractive alternative to the experimentally difficult infrared spectroscopic techniques which have been commonly employed in acyclic conformational analysis. In favorable cases, it has proved possible to determine the relative populations of rotational conformers in solution directly, by examining the sample at temperatures sufficiently low to slow the rate of conformational interconversion to less than the value required to average the resonances due to the separate conformers.4 However, even for compounds with which such low-temperature studies are impractical, examination of the magnitudes and temperature dependence of vicinal spin-spin coupling constants may provide an indirect method of examining the populations of rotational conformers in solution.6p6 The work reported in this paper is concerned with the conformational analysis of derivatives of 3,3-dimethylbutane, using these indirect techniques. Methods and Results Derivatives of 3,3-dimethylbutane substituted at the 1 position exist in solution as a rapidly interconverting (1) This research was supported by the National Science Foundation through Grant No. GP-2018, and through its undergraduate research participation program. Calculations were carried out in part at the Massachusetts Institute of Technology Computation Center, Cambridge, Mass. (2) See, for example, S. Mizushima, “Structure of Molecules and Internal Rotation,” Academic Press Inc., New York, N. Y . , 1954; N. Sheppard, Adcan. Spectry., 1, 288 (1959). The extinction coefficients for vibrational absorption bands in infrared studies have proved particularly difficult to determine accurately in solution: A. W. Baker, H. 0. Kerlinger, and A. T. Shulgin, Spectrochim. Acta, 20, 1467 (1964). (3) E. L. Eliel, N. L. Allinger, S . J. Angyal, and G. A. Morrison, “Conformational Analysis,” Interscience Publishers, Inc., New York, N. Y . , 1965. (4) R. A. Newmark and C. H. Sederholm, J . Chem. Phys., 43, 602 (1965), provide a careful demonstration of this technique. (5) H. S. Gutowsky, G. G. Belford, and P. E. McMahon, ibid., 36, 3353 (1962). (6) N. Sheppard and J. J. Turner, Proc. Roy. SOC.(London), A252, 506 (1959).
mixture of one trans and two gauche conformers around the C1-C2 bond (I, 11, 111). The nmr spectra of the
x I
H I1
H
I11
methylene protons in these compounds is not complicated by coupling with the protons of the t-butyl group. In the absence of coupling to nuclei in the substituent group X, the methylene protons can be treated as AA’XX’ or AzXz spin systems, and their spectra described using a maximum of four coupling constants: two vicinal coupling constants J and J’,and two geminal coupling constants J A and JX.’ Examination of the vicinal coupling constants provides a method of investigating the populations of I, 11, and 111. The magnitude of J or J’ in a 1,2-disubstituted ethane is determined primarily by the corresponding HCCH dihedral angle, and is in consequence dependent on the relative populations of the trans and gauche conformations.8 Abraham and Bernstein have shown that if J - J’ < [~Av~/,(JA - Jx)]‘”
(1)
the spectrum of the methylene protons will appear as an AzXzspectrum (Ami2is the width at half-height of the component line^).^ If J - J’ is greater than the quantity given in eq 1, the spectrum of the methylene protons will be an AA’XX’ spectrum, and analysis of the spectrum may yield values for each of the coupling constants. Unfortunately, the electronegativity and polarizability of substituents, and structural features of the molecule other than the HCCH dihedral angle, influence these coupling constants in a manner which is difficult to predict quantitatively.8 As a result of this uncertainty, the relative magnitudes of the vicinal coupling constants cannot be relied on in the absence of other information to provide an accurate measure of conformer populations. However, examination (7) The nomenclature used is that employed by Pople, et al., and by Roberts: J. A. Pople, W. G. Schneider, and H. J. Bernstein, “High Resolution Nuclear Magnetic Resonance,” McGraw-Hill Book Co., Inc., New York, N. Y., 1959, Chapter 6; J. D. Roberts, “An Introduction to the Analysis of Spin-Spin Splitting in High Resolution Nuclear Magnetic Resonance Spectra,” W. A. Benjamin, Inc., New York, N. Y . , 1962, Chapter 4. (8) For a recent review, see: M. Barfield and D. M. Grant, Adcan. Mugnelic Resonance, 1, 149 (1965); M. Karplus, J . Am. Chem. Soc., 85, 2870 (1963). For proton-fluorine couplings, the issue is less clear: R. J. Abraham and L. Cavalli, Mol. Phys., 9,671 (1965). (9) R. J. Abraham and H. J. Bernstein, Ca#.J . Chem., 39, 216 (1961).
Whitesides, Sevenair, Goetz / Isomerism in Derivatives of 3,3-Dimethylbutane
1136
--
3
1 ' , 3O0r1 2 o c II O
IC
+
z 100-
a
+ ln
z
m
9 0 L
i
constants are needed to describe the coupling in the individual conformers. The assumption that two gauche and one trans coupling constants are sufficient to describe these couplings is equivalent to saying that the XCCH dihedral angle is the most important parameter in determining the influence of X on the magnitude of the vicinal coupling constants. With these approximations, the observed coupling constants J and J' can be expressed in terms of the coupling constants of the individual rotational conformers Jt, J g g , and Jgt.
+ nII(Jgg + Jgt) (1 - 2 n d J g g + n d J t + Jgt)
J = (1
-I
7.0t
J' =
- 2nII)Jt
nII = exp(-AE/RT)/[l I
3.0l
I -50
I 0
I 50
I
I
100 150 200
TEMPERATURE
'
('C)
Figure 1. Temperature dependence of the vicinal coupling constants of 1-substituted derivatives of 3,3-dimethylbutane. The solid curves are the theoretical temperature dependences, calculated using the parameters in Table I. The upper set of curves represent values for J. the lower set J'.
of the temperature dependence of the vicinal coupling constants does provide a direct method of determining the position of rotational conformational e q ~ i l i b r i a . ~ , ~ The coupling constants J and J' are averages over vicinal couplings in each of the rotational conformers I, 11, and III. In theory, the gauche and trans coupling constants in each of these conformers might be different. We will make the approximation that only three different coupling constants are necessary to describe all of the spin-spin interactions in the three conformers: one trans ccupling constant Jt, which is the same in both gauche and trans conformers; and two gauche coupling constants J g g and Jgt which describe the coupling between gauche protons when the substituent X on C1 is gauche or trans, respectively, to the proton on Cn (IV, V). The justification for the use of only
+ 2 exp(-AE/RT)]
(2) (3) (4)
Here nII is the mole fraction of one of the gauche conformers, and A E is the difference in energy between gauche and trans conformers. Equation 4 assumes that Eyauche > Etmw Explicit values for each of the four parameters in these equations can be obtained from the experimentally determined temperature dependence of the vicinal coupling constants by a least-squares procedure, in which the function cp
three limiting coupling constants follows from the clear experimental5,lo and theoretical8 evidence that the influence of the substituent X on the magnitude of the vicinal proton-proton coupling constant in an X C H C H fragment also depends upon the XCCH dihedral angle. Since this angle is approximately 60" for both ,3 protons in the trans conformer I and for one of the ,3 protons in conformers 11 and 111, but approximately 180" for the remaining proton in conformers I1 and 111, at least two different limiting gauche coupling
is minimized by systematic variation of the parameters AE, Jt, Jgg,and Jgt. Here, J and J' are respectively the larger and smaller of the observed vicinal coupling constants at each measured temperature T,, and Jcalcd and J'calcd are the corresponding values calculated using ey 2, 3, and 4 with trial values for the unknown parameters. Our calculations (carried out using an iterative FORTRAN 11 program), made the assumptions that measurements at each temperature T , carried equal weight, and that the errors in the temperatures could be neglected. The values obtained for Jt, Jgt,and J g g by applying this procedure to the temperature dependence of the vicinal coupling constants of nine derivatives of 3,3-dimethylbutane are shown in Table I. For comparison and for future reference, the results of a similar three-parameter analysis in which J g g was assumed equal to Jgtare included in this table; the single gauche coupling constant in the three-parameter analysis was called Jg. Equal values were obtained for A E using either the three- or the four-parameter procedures ; these values are listed in Table IV, together with values obtained by approximate methods described below. Figure 1 shows the agreement obtained between the observed temperature dependence for the vicinal coupling constants for several of these compounds, and that calculated using the values of AE and the coupling constants obtained from the four-parameter analysis. The probable error in the parameters from the leastsquares analysis can be estimated using a procedure suggested by Gutowsky.6 In this procedure, cp is expanded in Taylor series in the neighborhood of the minimum value p0 obtained during the least-squares variation on the parameters.
(10) I2 ( 6 J 0 2 T,
(8)
In evaluating eq 8 in this work, we estimated somewhat arbitrarily that the experimental uncertainty in each of the observed vicinal coupling constants was 0.2 cps. Since cpo is known, the probable error AJ, in Jt can then be obtained using eq 7. The second derivatives used in estimating the error in each of the parameters in the four-parameter analysis can be obtained by differentiating eq 2-5.
b2nrI - - - exp(-AEIRT) - 4 exp(- 3LEIRT) bAE2 R2TZ[1 2 exp(-AE/RT)14
+
(%)'
=
exp( - 2AE/RT) R2T2[1 2 exp(-AE/RT)14
+
(1 lb) (1 IC)
The uncertainties in the parameters obtained from the variable-temperature analysis and given in Table I
N is
and Table IV were estimated using this procedure. Errors are listed as, e.g., J, f AJ,. It is worthwhile to point out explicitly that this procedure makes no attempt to estimate the magnitudes of systematic errors incorporated into the variable-temperature analysis. It is of interest that both Jt and J g g in Table I appear to be insensitive to the character of the substituent. The total variation observed in these constants is 0.8 cps, and is of the same order of magnitude as their uncertainty. Moreover, the deviations from their average values bear no obvious relation to any property of the substituent. In contrast, Jgt appears to be moderately sensitive to substituent electronegativity, although the probable error in this constant is appreciably larger that that in Jggor Jt. The total variation in the magnitude of Jgtis comparable with that observed for a corresponding range of substituents in substituted bicyclo[2.2. llheptenes, lo although less than that observed for substituted ethylenes.I2 Approximate Methods. The least-squares analysis of the temperature dependence of the vicinal cocpling constants is the most accurate method presently available for obtaining the magnetic and thermodynamic parameters describing the rotational conformers of 1,2-disubstituted ethanes from nmr data. Unfortunately, collection and analysis of accurate variabletemperature data is time consuming. Consequently, two more approximate methods requiring only ambient temperature spectra have been used to obtain approximate values for A E for other common organic substituent groups. The first of these methods was proposed by Snyder and is based on the assumption that the magnitude of a vicinal coupling constant can be related approximately to the corresponding HCCH dihedral angle q5 by eq 12. l 3 Jvic=
where
b
A
+B
COS'
q5
(12)
The form of this equation is that originally obtained by Karplus, l 4 with the additional assumption that only one value of the constant A is required over the range of dihedral angles encountered. With this assumption (12) C. N. Banwell and N. Sheppnrd, Mol. Phjs., 3, 351 (1960); Discussions Faraday SOC.,34, 115 (1962); T. Schaefer, Can. J . Chem., 40, l(1962). (13) E. I. Snyder, J. Am. Chem. SOC.,88, 1165 (1966). We wish to thank Dr. Snyder for sending us a copy of this paper prior to its publication. (14) M. Karplus, J. Chem. P h j . ~ .30, , 11 (1959).
Whitesides, Sevenair, Goetz
Isomerism in Derivatiues of 3,3-Dimethylbutane
1138 Table 11. Chemical Shifts (cps) and Coupling Constants (cps) Obtained from the Ethylene Proton Spectra of 3,3-Dimethylbutyl Derivatives at 60.0 Mc/sec and 32" Substitutent
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.
AIRz*n(EtiO)c MgR .n(EtzO)c Si(CH3)3 ZnR .n(Et,O)c
I P/C&)z CsHj NH(CH&+S03HNHa+S03HCDzOH SCH3 SCN SC6Hs Br CONHz HgRe Phthalimide HgCl CO,-K+
c1
C02H NH2 COCH, C02CH3 COCl NHCHO N(CH& CN OH OCsH6 F
J4
J'Q
14.2 14.2 13.9 13.3 13.0 13.0 12.9 12.9 12.7 12.3 12.3 12.2 12.1 12.1 11.9 11.8 11.6 11.6 11.6 11.3 11.2 11.1 11.1 11.0 10.9 10.8 10.7 10.2 9.5 7.2 6.5
3.9 4.2 4.0 4.7 4.8 4.3 4.7 4.7 4.8 4.6 4.8 4.7 4.7 5.1 5.1 5.1 5.2 5.3 5.3 5.4 5.4 5.1 5.2 5.6 5.4 5.4 5.0 5.8 5.8 7.2 6.5
JB'
J A ~
13.4 13.4 13.9 13.6 13.6 13.3 13.6 (13.7 (13.3 14.0 13.6 13.4 13.4 14.0 13.6 13.6 13.4 (12.8 13.9 13.6 13.8 13.1 13.9 13.7 13.7 (12.6 (13.0 13.8 13.5
13.4 12.5 13.9 12.4 9.2 13.3 13.3 13.7)d 13.3)d 14.0 12.4 12.2 12.3 9.9 14.6 12.5 13.3 10.4)d 13.9 10.5 15.6 11.7 16.4 15.2 16.5 12.6)d 11.6)d 17.0 10.3 e e
e
e
AVb
-87.0 - 124 -44.7 80.2 72.2 40.9 62.0 88.5 82.1 15.5 54.6 67.2 76.0 86.7 38.6 34.2 122.1 17.6 39.7 104.1 42.4 78.7 55.0 40.3 70.5 103,5 90.7 40.1 128.7 134 172
Solvent (CH3CHhO (CH~CHZ)~~
cc1,
(CH3CH2)20 CCl, C6H6 CCI, DzO D20 CC14
cc1, cc14 cc14
CCI, CDCI, (CHKH&O CDC13 CDCli D10 CCI, CCl, C5H5 CCI, CCl, CCl, CCl, C5H6 CCI, CCll CCI, CCI,
Solvent concn,
1 1-6 20 1
20 20 20 20 20 20 20 20 20 20 10 5-15 10 10 20 20 20 20 20 20 20 20 20 20 20 20 20
a The geminal and vicinal coupling constants were assumed to have opposite signs. The uncertainty in the vicinal coupling is estimated to be no larger than 1 0 . 2 cps; the uncertainty in the geminal coupling constants is larger. * A positive sign for Av implies that the (CH3)8CCH, resonance occurred at higher field than the CH2Xresonance. c M. Witanowsky and J. D. Roberts, J. Am. Chem. Soc., 88, 737 (1966). R is 3,3-dimethylbutyl. Obtained using assumptions described in the Experimental Section. J.& - JB is meaningful for these; the absolute magnitudes are only approximate. e Geminal coupling constants cannot be obtained by direct analysis of A2Xzspectra.
it is easily shown that l 3
AE
=
RT In 2nI/(l - nr)
(13)
where
+
+
+
0.5r[cos2(120 - 4) cos2 (120 4) - cos2 41 1 - cos2 d - r(0.25 0.5[cos2'(120 - +)+ cos2 (120 +)I} d r - 1) B(l - cos2 4 - r(0.25 (14) 0.5[cOS2 (120 - 4) COS' (120 4)]])
nI
=
+
+
+
and r = J/J'. Here 4 is defined as the dihedral angle between the t-butyl group and the substituent in a gauche conformation, and nI is the mole fraction of the trans conformer I. The value of AIB used in eq 14 in this work was 0.05, and was estimated by inserting the average values of Jt and Jg obtained from the three-parameter leastsquares data in Table I into eq 12, with appropriate values for the dihedral angle.
Jt = A Jg = A
+ B C O S180 ~ = 14.0 + B 60" = 4.0 COS'
The value for r was obtained for each substituent by analysis of the ambient-temperature spectra using conventional methods; chemical shifts and coupling constants for the derivatives of 3,3-dimethylbutane examined are listed in Table 11. The spectra of most of Journal of the American Chemical Society
89:5
these compounds were of the AA'XX' type, and analysis yielded all four coupling constants. These coupling constants appear to be relatively insensitive to solvent and concentration. For example, the results of analysis of the spectrum of 3,3-dimethylbutyl iodide in several solvents are given in Table 111. The variation in the coupling constants reported in this table is typical of that observed for other of the compounds in Table 11 on changing solvent and concentration, and serves to indicate the reproducibility of the spectra. In all of these spectra, the geminal coupling constant J A is assigned to the methylene group directly bonded to the t-butyl group, since its magnitude is essentially independent of the substituent. The values obtained for AE by setting C#I in eq 14 equal to 65" and using the coupling constants in Table I1 are listed in Table IV,15 The agreement between the values of AE obtained by this approximate method and the values obtained by the least-squares analyses is good. The probable errors in the parameters obtained using this method have been discussed in detail by Snyder.l3 (15) The dihedral angle, 6,in conformers I1 and I11 should probably be greater than 60°, since nonbonded repulsions between the r-butyl group and the substituent in the gauche conformations should distort this conformation from a perfect staggered geometry. However, the proper value for 4 should almost certainly vary with the bulk of the substituent. The value 6 = 65" was chosen somewhat arbitrarily since it seemed to give values for A E in good agreement with those obtained from the temperature-dependence studies. See also ref 13 for a discussion of this point.
March I, 1967
-
-
-
For r 2.0 and 4 60°,AE is estimated to change by 0.01 kcal per degree of change in 4. Similarly, for 65" and r 2.5, a change in r of 0.05 (corresponding approximately to a variation of J' by 0.1 cps) changes the estimated magnitude of AE by 0.03 kcal/mole. These estimates suggest that the magnitude of the uncertainty in the values of AE obtained using eq 13 and 14 (Table IV) is approximately 2 0 z . Despite the agreement between the values of AE derived from the least-squares analysis and those obtained from eq 13 and 14, it seemed advisable to have an alternative method of estimating AE from the room temperature coupling constants, which avoided some of the assumptions made by the latter procedure.'6 The approach used was an empirical one which took advantage of the previously demonstrated insensitivity of Jt, J g g , and Jgtto the nature of the substituent. The assumption was made that the average values of these limiting coupling constants (Table I) would provide satisfactory approximations to the coupling constants in individual rotamers for all of the substituents listed in Table 11. This assumption is certainly reasonable for Jt and J g g , both of which seem to be essentially independent of the substituent; a small error (estimated below) is probably introduced into AE by making this assumption for Jgt. With this assumption, a curve relating A E to J and J' could be calculated easily using eq 2-4 (Figure 2, curve B). Estimates of AE could then be obtained for each of the compounds in Table I1 by comparing the observed values of J and J' separately with this curve. Usually the value of AE estimated from J differed from that estimated from J' by 0.1 to 0.5 kcal/mole; each value of AE listed in the second column of Table IV is an average of the estimates from the individual coupling constants. These estimates agree well with those obtained using the two methods described previously. In order to estimate the influence of J: on the value of AE determined using Figure 2, curves similar to that calculated for the average values of Jt, Jp",.and Jgt were calculated using the extreme values obtained for Jgt from the least-squares analysis (Figure 2, curves A and C). These curves indicate that for values of AE ranging from approximately 0.7 kcal/mole to 2.0 kcal/mole, a change of 3.4 cps in the value of Jgt used in constructing curve B would change the values of AE estimated using this procedure by approximately 0.2 kcal/mole.
-
1139
Discussion Observation of an AA'XX' type spectrum for the methylene protons of the substituted 3,3-dimethylbutanes listed in Table I1 establishes immediately that their most stable conformation is the one having the t-butyl group and the substituent trans. A favored gauche conformation would necessarily result either in an AzXz spectrum (if conformational interconversion were rapid on the nmr time scale) or a more complicated ABXY spectrum (if interconversion were slow). A number of factors have significant bearing on the accuracy of the energy differences between the trans and gauche conformations estimated using the methods
+
(16) In particular, eq 12 is probably inferior to Jvio = A cos q5 B cos* 9 as the functional relation between J and 9 , See M. Barfield, J . Chem. Phys., 44, 1836 (1966), and ref 8.
2
100
0.0
1.0
2.0
3.0
4.0
AE ( K C A L / M O L E )
Figure 2. The dependence of J (upper curves) and J' (lower curves) on AE, calculated using eq 2-4. The values used for Jt and Jge were 14.1 and 4.2 cps, respectively. The values for Jet were curve A, 4.7 cps; curve B, 3.1 cps; curve C, 1.3 cps.
discussed above. Of these methods, analysis of the temperature dependence of the vicinal coupling constants is undoubtedly the most accurate. This method requires no important assumptions concerning the effect of substituent electronegativity on coupling constants, or concerning the form of the function relating the coupling constants in the individual rotational conformers to the observed averaged coupling constants. However, it does assume that the contributions of temperature-dependent amplitudes of vibration to the observed temperature dependence of the vicinal coupling constants can be neglected, and that the bond angles and bond lengths in the individual conformers do not change significantly with temperature. Further, it depends upon the accurate measurement of small changes in the observed coupling constants. In order to estimate the reliability of this method, it is important to consider the magnitudes of some of the other effects which might contribute to the temperature dependence of the vicinal coupling constants. Gutowsky and co-workers have estimated theoretically the magnitudes to be expected from temperaturedependent vibrational contributions to both vicinal17 and geminal18 proton-proton coupling constants. With several assumptions concerning the form of the torsional potential function V(q5), these workers concluded that the vicinal coupling constant Jt in an aliphatic molecule would increase by approximately 0.3 cps on increasing the temperature from 200 to 400°K as a result of increasing amplitude of the torsional motion, and that Jg would decrease over this temperature range by a corresponding amount. These contributions to the observed coupling constants are expected to cancel exactly when V(4) has threefold symmetry, and experimental measurements of torsional contributions to proton-proton coupling constants in several substituted ethanes have confirmed this expectation. l 7 , I 9 In the less symmetrical molecules discussed (17) J. C . Schug, P. E. McMahon, and H. S . Gutowsky, J . Chem. Phys., 33, 843 (1960). The HCCH dihedral angle dependence of J was
assumed to follow eq 12. (18) H. S. Gutowsky, V. D. Mochel, and B. G . Somers, ibid., 36, 1153 (1962). (19) J. G. Powles and J . H. Strange, Discussions Faraday Soc., 34, 30 (1962). A small torsional temperature dependence has been observed for fluorine-fluorine couplings. W. S. Brey, Jr., and K. C. Ramey, J. Chem. Phys., 39, 844 (1963). See also J. .Toni< and H. S. Gutowsky, ibid., 42, 140 (1965).
Whitesides, Seuenair, Goetz
Isomerism in Derivatives of 3,3-Dimeth ylbutane
1140
this paper, cancellation of the torsional contributions to Jt and J g is expected to be incomplete. Nonetheless, the calculated dependence of Jt and J , on temperature is sufficiently small that torsional contributions t o the temperature dependence of the vicinal coupling constants can probably be ignored. I t is diflicult to estirnate the importance of changes with temperature of mean bond lengths or angles other than the torsional angle 4. However, it is interesting to note in this connection that for each of the compounds listed in Table 11, the magnitude of the obserced geminal coupling constants increased by 0.0 to 0.4 cps on increasing the temperature 100". A temperature dependence of this magnitude is larger that that predicted from estimates of the corresponding increase in the amplitude of the H-C-H bending vibrations, 'I and might reflect changes in molecular geometry which would also influence the vicinal coupling const'inls. However, the observed variation may also be connected with a difference in the effect of the substituents on the geminal coupling constants in the gauche and t r a m conformers, ?O or with temperature-dependcnt changes i n bulk properties of the solution. The c!ata in Table 111 suggest a similar and probably real sensitivity of JAkto changes in the solvent;21 the sollent variation of this coupling constant is not accompanied by similar variation in Jn, J, or J ' .
in
Table 111. Solvent Dependence of the Coupling Constants (cps) and Chemical Shift (cps) for 3,3-Dimethylbutyl Iodidea
J A ~
Solvent
Jb
J'&
JB*
AU
1. Cyclohexane 2. Carbon tetrachloride 3. 3,3-Dimethylbutyl iodide 4. Carbondisulfide 5. Chloroform 6. Benzene 7. Acetic acid 8. Acetone 9. Nitrobenzene
13.00 12.99
4.76 4.80
13.63 13.60
9.15 9.17
76.6 72.2
13.05
4.79
13.55
9.12
73
12.95 13.03 13.01 12.92 12.99 12.93
4.79 4.79 4.74 4.80 4.81 4.73
13.52 13.50 13.50 13.47 13.43 13.36
9.14 9.17 9.17 9.15 9.20 9.14
72.4 74.2 49.4 76.3 78.8 76.4
1 All solutions were approximately 10% 3,3-dimethylbutyl iodide Geminal and vicinal coupling constants are assumed by volume. to have opposite sign.
known geometry, predict values for Jt and Jg in good agreement with those observed. 2 2 These observations suggest that the geometry of the carbon framework of 3,3-dimethylbutane is not appreciably distorted by the introduction of large substituent groups such as phenyl and trimethylsilyl at C1. Second, the relation observed between Jgt and the electronegativity of the substituent is in qualitative accord with that which has been thoroughly established in molecules of known g e ~ m e t r y . If~ ~changing ~ ~ ~ ~the ~ ~substituent ~ ~ attached to the 3,3-dimetnylbutyl grouping resulted in important changes in the molecular geometry of the individual gauche and trans conformers, these changes might have been expected to produce more pronounced deviations in the relation between Jgtand electronegativity than those observed. On the basis of these considerations, it seems reasonable to accept the values of LIE obtained using the leastsquares analyses as meaningful estimates of the energy difference between trans and gauche conformations of substituted 3,3-dimethylbutanes. Moreover, both the similarity between the values of Jt and J g g obtained with different substituents, and the recognizable dependence of Jgt on electronegativity, indicate that the fourparameter analysis provides an accurate zstimate of the coupling constants in the gauche and t r a m conformations of these molecules. The remarkable insensitivity of these coupling constants to substituent effects lends support to the usefulness of the two approximate procedures used to obtain estimates of AE for those compounds whose spectral temperature dependence was not explicitly examined, since important assumptions in both of these procedures required the neglect of substituent effects of this type. The agreement between these approxiniate values of AE and those from the least-squares analysis further supports the reliability of the approximate values. It is of some importance to the study of conformational analysis in acyclic molecules that the order of "size" of the groups established by these methods shows significant differences from that determined by exaniination of their relative order of preference for the equatorial position on a cyclohexane ring. Figure 3 indi=
Two observations concerning the magnitudes of Jt, J g g , and Jgt obtained from the least-squares procedure indicate that the geometry and bonding in the derivatives of 3,3-dimethylbutane examined in this study is unexceptional, and consequently that coupling constants and conformational energies obtained in these compounds can legitimately be compared with those obtained in other substituted ethanes. First, the values obtained for Jt and J g g appear to be approximately the same for each of the compounds examined (Table I). Moreover, empirical functions describing the relation between the magnitude of a vicinal coupling constant and its corresponding dihedral angle, in molecules of ( 2 0 ) J. A. Pople and A. A. Bothner-By, J . Chem. Phys., 42, 1339 1965), provide a general discussion of substituent effects on geminal coupling constants. (21) Geminal coupling coinstants have been observed to vary with solvent even in molecules of rigid geometry. See, for example, V. S. Watts, G. S. Reddy, and J. H. Goldstein, J . Mol. Spectry., 11, 325 (1963); I
